Equidimensionality

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In mathematics, especially in topology, equidimensionality is a property of a space that the local dimension is the same everywhere.[1]

Definition[edit]

A topological space X is said to be equidimensional if for all points p in X the dimension at p that is, dim p(X) is constant. The Euclidean space is an example of an equidimensional space. The disjoint union of two spaces X and Y (as topological spaces) of different dimension cedes an example of a non-equidimensional space.

Cohen–Macaulay ring[edit]

An algebraic variety whose coordinate ring is a Cohen–Macaulay ring is equidimensional.[2]

References[edit]

  1. ^ Wirthmüller, Klaus. A Topology Primer: Lecture Notes 2001/2002 (PDF). p. 90. 
  2. ^ Anand P. Sawant. Hartshorne’s Connectedness Theorem (PDF). p. 3.